TIME & WORK : Formula & Tricks
TIME & WORK
1. Basic Formula
Work (W) = Rate x Time , Rate (n) = Work / Time, Work = Constant
2. LCM Method (Most Important)
Q. A can do a work in 10 days, B in 20 days. Find time taken by A + B.
Soln
LCM of 10 & 20 = 20 units
A's 1 day work 20/10 = 2 units/day, B's 1 day work 20/10 = 1 unit/day
A + B = 3 units / day, Time = 20/3 days (Ans)
3. Three Person Concept
Q. A = 15 days, B = 20 days, A+B+C=8 days , Find C alone.
Soln
LCM of 15, 20, 8 = 120 units
A = 120/15 = 8 units/day
B = 120/20 = 6 units/day
A + B + C = 120/8 = 15 units/day
C = 15 - (8+6) = 1 unit/day
Time = 120/1 = 120 days (Ans)
4. Leaving Midway
Q. A = 10 days , B = 20 days They work for 4 days, B leaves. Find remaining time by A.
Soln
LCM = 20 units, A = 20/10 = 2 units/day, B = 20/20 = 1 unit/day
Work in 4 days = (2+1)x4 = 12 units , Remaining work = 20 – 12 = 8 units
A alone time 8/2 = 4 days (Ans)
5. Man x Day Work
Men x Days = Constant
M1D1 = M2D2
Q. 25 men = 12 days, 30 men = ? days
Soln
25 * 12 = 30x
x = 25 x 12/30 = 10 days (Ans)
6. Men & Women Problems
Q. 15 men + 20 women → 10 days, 24 men +32 women = ?
Soln
Let 1 man = 2 units, 1 woman = 1 unit
Team - 1 work = (15x2+20x1) = 50 units/day
Team - 2 work (24×2+32x1) = 80 units/day
Total Work = 50 * 10 = 500 units
Days = 500/80 = 6.25 days (Ans)
7. Concept of MDH (Man x Day × Hours)
Work = M x D x H
Q. A = 6 days, 5 hrs/day (Total hrs = 30), B = 15 days, 3 hrs/day (Total hrs = 45)
A+B = ?
Soln
Total work LCM (30, 45) = 90 units
A = 90/30 = 3 units/hr , B = 45 = 2 units/hr
A+B = 5 units/hr
Time = 90 / 5 = 18 hrs (Ans)
8. Efficiency Concept
Q. If A is 60% more efficient than B
Soln
A : B = 160 : 100 = 8 : 5
The ration = 5 : 8
9. Alternate Days
Q. A20 days, B = 30 days, Work on alternate days starting with A.
Soln
LCM 60 units, A = 3 units/day B = 2 units/day
1st day (A) = 3, 2nd day (B) = 2
2 days work = 5 units
60 / 5 = 12cycles
Time = 12x2 = 24 days (Ans)
10. Strange question (Cats & Rats)
Q. 100 cats kill 100 rats in 100 days How many days for 10 cats to kill 10 rats?
Soln
Same Ratio Same Time
100 days (Ans)